US Secretary of State Condoleezza Rice has told Israel it must make "hard decisions" to advance the peace process with the Palestinians.
Ms Rice lays a wreath at the Yad Vashem Holocaust memorial
Ms Rice arrived on Sunday for talks with Israeli Prime Minister Ariel Sharon, before meeting Palestinian leader Mahmoud Abbas on Monday.
Her visit comes amid renewed hopes for progress, as Mr Sharon and Mr Abbas are due to hold talks in Egypt on Tuesday.
Ms Rice said this was "a time of optimism" in the Middle East.
Ahead of talks with Israeli Foreign Minister Silvan Shalom, she said: "We will ask of our partners and our friends in Israel that Israel continues to make the hard decisions that must be taken to promote peace and... the emergence of a democratic Palestinian state."
She said: "This is a time of opportunity and a time we must seize."
Mr Shalom told Israeli TV after the meeting that he had spoken to Ms Rice about Israel's demands of the Palestinians.
"If the Palestinians do not do everything to halt the smuggling of weapons through tunnels, close the tunnels, close the weapons workshops, gather up illegal weapons - we would simply be giving the violent groups time to regroup and carry out terror attacks that could collapse the whole process," he said.
The death of Yasser Arafat in November and last month's election of Mr Abbas have radically changed the political landscape in the Middle East.
Both Mr Sharon and the US had refused to negotiate with Arafat, branding him an obstacle to peace.
RICE'S SEVEN-DAY TOUR
Fri: Met UK's Tony Blair and Foreign Secretary Jack Straw in London; talks with Germany's Gerhard Schroeder in Berlin
Sat: Talks with leaders in Germany, Poland and Turkey; met Russian foreign minister in Ankara
Sun: Met Turkish government, then on to Israel. Met Ariel Sharon
Mon: Talks with Mahmoud Abbas in West Bank
Tue: Meets Silvio Berlusconi in Rome, then delivers speech in Paris
Wed: Talks with French ministers, then on to meet Nato and EU officials in Brussels and Luxembourg
Thurs: Returns to Washington
The US has strongly praised the Palestinian election as a step towards democracy and has welcomed the efforts of Mr Abbas to get militant factions to agree to an informal cessation of hostilities.
Ms Rice headed to Israel from Turkey - part of her seven-day tour of Europe and the Middle East.
Her trip comes at an opportune moment, says the BBC's Dan Isaacs in Jerusalem. But he adds that the climate is still one of caution and deep mistrust, despite the feeling that change may be in the air.
In an interview with the BBC, Ms Rice praised Mr Abbas's election as "a real plus for the [peace] process".
"He [Abbas] has a lot of work to do, of course, to really stop terrorism and to also make sure that terrorist groups cannot just turn terrorism on and off as they wish," Mr Rice told the Breakfast with Frost programme.
She said the Palestinians "will need help in building the institutions that will become the foundation of a state". And Israel needed to create conditions to bring this state about.
She has urged the two sides to keep making progress on their own.
Mr Abbas and Mr Sharon met on several occasions in the summer of 2003 during Mr Abbas's brief spell as prime minister, including at the launch of the now stalled international peace plan known as the roadmap.
But their meeting on Tuesday will be the highest-level talks between the Israelis and Palestinians since the intifada broke out in 2000.
A stumbling block to the talks was removed on Saturday evening when the two sides agreed to set up a joint committee to assess the list of about 900 Palestinian prisoners Israel has promised to free.